Abstract

Four modal methods of reconstructing a wavefront from its difference fronts based on Zernike polynomials in lateral shearing interferometry are currently available, namely the Rimmer–Wyant method, elliptical orthogonal transformation, numerical orthogonal transformation, and difference Zernike polynomial fitting. The present study compared these four methods by theoretical analysis and numerical experiments. The results show that the difference Zernike polynomial fitting method is superior to the three other methods due to its high accuracy, easy implementation, easy extension to any high order, and applicability to the reconstruction of a wavefront on an aperture of arbitrary shape. Thus, this method is recommended for use in lateral shearing interferometry for wavefront reconstruction.

Characteristics of the different shear ratios: (a) condition numbers of the four methods; (b) RMS reconstruction errors of the four methods under 1% modal noise; (c) noise levels of the difference fronts in the x and y directions under a certain absolute noise; and (d) RMS reconstruction errors of the four methods under the same noise as that in (c).